An electromechanical system in one example measures a parameter. The electromechanical system may comprise a micro-electromechanical system (“MEMS”) accelerometer or gyroscope that measures the parameter. For example, the accelerometer measures an acceleration and the gyroscope measures an angular rate (e.g., rotation). The gyroscope in one example comprises a vibrating beam with high Q degenerate fundamental modes of vibration. For example, high Q vibrating beams require little energy to sustain vibration. The vibrating beam in one example is employable for high performance closed loop angular rate sensing. The vibrating beam in another example is employable for lower performance open loop angular rate sensing. The mathematical model of the symmetrical vibrating beam is in many aspects similar to a vibrating ring or hemispherical resonator gyroscope (“HRG”). The analytical similarity to the hemispherical resonator gyroscope indicates that the vibrating beam gyroscope has the potential of achieving similar performance.
Drive components coupled with the vibrating beam cause a first oscillation of the vibrating beam. An angular rate of the vibrating beam and the first oscillation induce a Coriolis force on the vibrating beam. For example, the angular rate is about the longitudinal axis of the vibrating beam. The Coriolis force causes a second oscillation of the vibrating beam 102. The second oscillation is substantially perpendicular to the first oscillation. Feedback components in one example provide feedback on a magnitude of the first oscillation to the drive components for regulation of the first oscillation. Pickoff sensor components sense the second oscillations and apply control signals to null the pickoff signal. The control signals are a measure of the magnitude and polarity of the angular rate of the vibrating beam.
The drive/pickoff components oscillate the vibrating beam and control the amplitude of vibration in a first direction and the pickoff/drive components sense and control the second oscillation from a second direction. As the vibrating beam is driven in one direction, misalignments associated with manufacturing tolerances and electronic phase errors in the servo electronics may cause vibration in the sense direction which is interpreted as angular rate. Variations in the magnitude of the misalignment or the phase of the servo electronics over time and temperature introduce gyroscope bias drift error. As one shortcoming, since the drive oscillation of the vibrating beam remains in the first direction during operation, bias errors are introduced over time and varying temperature. Differences in the damping time constants between the drive and sense directions of the vibrating beam due to gas squeeze film, thermal elastic, and mounting damping effects can be interpreted as angular rate. Variation in these differential time constants introduces gyroscope bias drift.
Thus, a need exists for an angular rate sensing gyroscope that promotes a reduction in bias drift error.